A Note on Global Optimization for Max-Plus Linear Systems

TL;DR

This paper refines the understanding of global optimization in max-plus linear systems by clarifying operations, simplifying solution criteria, and characterizing solution uniqueness and sets.

Contribution

It provides explicit explanations of operations, simplified formulas, and criteria for solution existence and uniqueness in max-plus linear system optimization.

Findings

Explicit operations involving infinity and real numbers clarified.

Simplified formulas for greatest lower bound and solvability criteria.

Criteria for uniqueness and characterization of all globally optimal solutions.

Abstract

This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving global optimization problems are explained explicitly. Secondly, the formula of the greatest lower bound and the criterion of solvability of globally optimal solutions are simplified. Thirdly, the criterion of uniqueness of globally optimal solutions and the set of all globally optimal solutions are presented.